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						<h1 id="firstHeading" class="firstHeading" lang="en"><span dir="auto">Projections</span></h1>
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								<div id="siteSub">From PanoTools.org Wiki</div>
								
												
				<div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><p><br />
Representing a spherical view of the world on a flat computer monitor or print requires some manner of mapping from the 3D spherical scene in which the camera and viewer are embedded to the 2D medium on which they are rendered.  The techniques used for mapping are of exactly the same type long used by map makers to project the entire globe, or portions of it, onto two dimensional maps.  There is no single, unique projection for representing sections of the sphere on the globe.  Instead, all projections have various attributes and limitations.  There are many classes of projections used for various purposes (e.g. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/MapProjection.html">Mathworld's Projection Page</a>), but only a few are traditionally used for panoramic imaging.
</p><p><br />
<b>First - a word of warning: If you are looking for a single projection, that will map a spherical (even partial) panorama on a flat surface without bending lines: This won't work!</b>
</p><p>This link explains well why it is impossible: <a rel="nofollow" class="external free" href="http://www.progonos.com/furuti/MapProj/Normal/CartDef/MapDef/mapDef.html">http://www.progonos.com/furuti/MapProj/Normal/CartDef/MapDef/mapDef.html</a>
</p><p>Some of the most common projections when working with Panoramic imaging are:
</p>
<div id="toc" class="toc"><div id="toctitle"><h2>Contents</h2></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="Projections.html#Cylindrical_projections"><span class="tocnumber">1</span> <span class="toctext">Cylindrical projections</span></a>
<ul>
<li class="toclevel-2 tocsection-2"><a href="Projections.html#Cylindrical_projection"><span class="tocnumber">1.1</span> <span class="toctext">Cylindrical projection</span></a></li>
<li class="toclevel-2 tocsection-3"><a href="Projections.html#Mercator_projection"><span class="tocnumber">1.2</span> <span class="toctext">Mercator projection</span></a></li>
<li class="toclevel-2 tocsection-4"><a href="Projections.html#Miller_projection"><span class="tocnumber">1.3</span> <span class="toctext">Miller projection</span></a></li>
<li class="toclevel-2 tocsection-5"><a href="Projections.html#Equirectangular_projection"><span class="tocnumber">1.4</span> <span class="toctext">Equirectangular projection</span></a></li>
<li class="toclevel-2 tocsection-6"><a href="Projections.html#Lambert_cylindrical_equal_area"><span class="tocnumber">1.5</span> <span class="toctext">Lambert cylindrical equal area</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-7"><a href="Projections.html#Azimuthal_projections"><span class="tocnumber">2</span> <span class="toctext">Azimuthal projections</span></a>
<ul>
<li class="toclevel-2 tocsection-8"><a href="Projections.html#Rectilinear_projection"><span class="tocnumber">2.1</span> <span class="toctext">Rectilinear projection</span></a></li>
<li class="toclevel-2 tocsection-9"><a href="Projections.html#Stereographic_projection"><span class="tocnumber">2.2</span> <span class="toctext">Stereographic projection</span></a></li>
<li class="toclevel-2 tocsection-10"><a href="Projections.html#Fisheye_projection"><span class="tocnumber">2.3</span> <span class="toctext">Fisheye projection</span></a></li>
<li class="toclevel-2 tocsection-11"><a href="Projections.html#Equisolid_projection"><span class="tocnumber">2.4</span> <span class="toctext">Equisolid projection</span></a></li>
<li class="toclevel-2 tocsection-12"><a href="Projections.html#Orthographic_projection"><span class="tocnumber">2.5</span> <span class="toctext">Orthographic projection</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-13"><a href="Projections.html#Other_projections"><span class="tocnumber">3</span> <span class="toctext">Other projections</span></a>
<ul>
<li class="toclevel-2 tocsection-14"><a href="Projections.html#Cubic_projection"><span class="tocnumber">3.1</span> <span class="toctext">Cubic projection</span></a></li>
<li class="toclevel-2 tocsection-15"><a href="Projections.html#Sinusoidal_projection"><span class="tocnumber">3.2</span> <span class="toctext">Sinusoidal projection</span></a></li>
<li class="toclevel-2 tocsection-16"><a href="Projections.html#Transverse_mercator_projection"><span class="tocnumber">3.3</span> <span class="toctext">Transverse mercator projection</span></a></li>
<li class="toclevel-2 tocsection-17"><a href="Projections.html#Pannini_projection"><span class="tocnumber">3.4</span> <span class="toctext">Pannini projection</span></a></li>
<li class="toclevel-2 tocsection-18"><a href="Projections.html#Architectural_projection"><span class="tocnumber">3.5</span> <span class="toctext">Architectural projection</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-19"><a href="Projections.html#External_links"><span class="tocnumber">4</span> <span class="toctext">External links</span></a></li>
</ul>
</div>

<h1><span class="mw-headline" id="Cylindrical_projections">Cylindrical projections</span></h1>
<p>Cylindrical projections resemble classic rectangular world maps. The horizontal <a href="Field_of_View.html" title="Field of View">Field of View</a> is anything up to 360 degrees, horizontal distance is proportional to pan or <a href="Yaw.html" title="Yaw">yaw</a> angle, vertical distance is related to the angle above or below the horizon.
</p>
<h2><span class="mw-headline" id="Cylindrical_projection">Cylindrical projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Big_ben_cylindrical.jpg" width="200" height="100" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_cylindrical.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_cylindrical.jpg">[*]</a></div><a href="Cylindrical_Projection.html" title="Cylindrical Projection">Cylindrical Projection</a> h360° v120°</div></div></div>This is the projection most commonly used for printed panoramas with a large range of longitude (&gt;120 degrees).  It can be envisioned by imagining wrapping a flat piece of paper around the sphere tangent to the equator, and projecting a light out from the center of the sphere.  A full range of longitude, up to 360 degrees, can be represented with a cylindrical projection, but near the poles, the images become very distorted, so a full range of latitude cannot be used.  See <a href="Cylindrical_Projection.html" title="Cylindrical Projection">Cylindrical Projection</a> for more.
<p><br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Mercator_projection">Mercator projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Big_ben_mercator.jpg" width="200" height="100" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_mercator.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_mercator.jpg">[*]</a></div>Mercator Projection<a class="external" href="http://wiki.panotools.org/index.php?title=Mercator_Projection&amp;action=edit&amp;redlink=1">[*]</a> h360° v140°</div></div></div>
<p>Mercator Projection<a class="external" href="http://wiki.panotools.org/index.php?title=Mercator_Projection&amp;action=edit&amp;redlink=1">[*]</a> is a <i>conformal</i> projection.  This shows less pronounced distortion than either <i>cylindrical</i> or <a href="Equirectangular_Projection.html" title="Equirectangular Projection">Equirectangular Projection</a> which otherwise look very similar. See <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/MercatorProjection.html">mathworld's page</a> for details
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Miller_projection">Miller projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Ben_Miller_cylindrical.jpg" width="200" height="100" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Ben_Miller_cylindrical.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Ben_Miller_cylindrical.jpg">[*]</a></div>h360° v147°</div></div></div>
<p>Miller is similar to <a href="Projections.html#Mercator_projection">Mercator projection</a> but with slightly more compression at the top and bottom of the image, this distortion is less pronounced than <a href="Equirectangular_Projection.html" title="Equirectangular Projection">Equirectangular Projection</a> making it a good format for printing.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Equirectangular_projection">Equirectangular projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Big_ben_equirectangular.jpg" width="200" height="100" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_equirectangular.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_equirectangular.jpg">[*]</a></div><a href="Equirectangular_Projection.html" title="Equirectangular Projection">Equirectangular Projection</a> h360° v180°</div></div></div>
<p>Also called the "non-projection", this is a representation of the sphere which maps longitude directly to the horizontal coordinate, and latitude to the vertical coordinate.  This projection is often used for the source images in panoramic viewers like PTViewer<a class="external" href="http://wiki.panotools.org/PTViewer">[*]</a>.  See definition for <a href="Equirectangular_Projection.html" title="Equirectangular Projection">Equirectangular Projection</a> for more.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Lambert_cylindrical_equal_area">Lambert cylindrical equal area</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Ben_Lambert_cylindrical_equal_area.jpg" width="200" height="63" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Ben_Lambert_cylindrical_equal_area.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Ben_Lambert_cylindrical_equal_area.jpg">[*]</a></div>h360° v180°</div></div></div>
<p>This projection is 'equal area', making it very compact and suitable for purposes where distortion isn't important, similar to <a href="Projections.html#Sinusoidal_projection">Sinusoidal projection</a>.
<br style="clear:both;" />
</p>
<h1><span class="mw-headline" id="Azimuthal_projections">Azimuthal projections</span></h1>
<p>Azimuthal projections have rotational symmetry around the centre of the image, these are the kind of images that are produced by the various kinds of camera lens.
</p>
<h2><span class="mw-headline" id="Rectilinear_projection">Rectilinear projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:152px;"><img alt="" src="150px-Big_ben_rectilinear.jpg" width="150" height="150" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_rectilinear.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_rectilinear.jpg">[*]</a></div><a href="Rectilinear_Projection.html" title="Rectilinear Projection">Rectilinear Projection</a> h110° v110°</div></div></div>
<p>This is a fundamental projection which can be envisioned by imagining placing a flat piece of paper tangent to a sphere and projecting a light out from its center.  Obviously, only less than 180 degrees of longitude can be represented with this projection (exactly 180 degrees would require an image of infinite width), and in practice, far less. 
</p><p>Most non-fisheye cameras produce a nearly rectilinear image over their field of view (albeit with varying amounts of unavoidable <a href="Lens_distortion.html" title="Lens distortion">distortion</a>).  The Rectilinear projection is often used for prints of panoramas which cover less than ~120 degrees of longitude, since straight lines are preserved.  See <a href="Rectilinear_Projection.html" title="Rectilinear Projection">Rectilinear Projection</a> for more.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Stereographic_projection">Stereographic projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:152px;"><img alt="" src="150px-Big_ben_stereographic.jpg" width="150" height="150" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_stereographic.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_stereographic.jpg">[*]</a></div><a href="Stereographic_Projection.html" title="Stereographic Projection">Stereographic Projection</a> h180° v180°</div></div></div>
<p><a href="Stereographic_Projection.html" title="Stereographic Projection">Stereographic Projection</a> is a <i>conformal</i> form of <a href="Fisheye_Projection.html" title="Fisheye Projection">Fisheye Projection</a> where the distance from the centre is <i>not</i> equivalent to the spatial angle.  This is much easier on the eye for printing and display purposes.
</p><p>Stereographic is limited to a maximum horizontal (and vertical) angle of 360 degrees, images over 330 degrees are pretty, but not very usable.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Fisheye_projection">Fisheye projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:152px;"><img alt="" src="150px-Big_ben_fisheye.jpg" width="150" height="150" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_fisheye.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_fisheye.jpg">[*]</a></div><a href="Fisheye_Projection.html" title="Fisheye Projection">Fisheye Projection</a> h180° v180°</div></div></div>
<p>In a <a href="Fisheye_Projection.html" title="Fisheye Projection">Fisheye Projection</a>, the distance from the centre of the image to a point is proportional to the equivalent spatial angle.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Equisolid_projection">Equisolid projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:152px;"><img alt="" src="150px-Ben_Equisolid.jpg" width="150" height="150" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Ben_Equisolid.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Ben_Equisolid.jpg">[*]</a></div>h360° v360°</div></div></div>
<p>This closely resembles a photograph of a mirrorball. Features are 'equal area' making it suitable for applications where distortion isn't critical. Equisolid is apparently the same as 'Lambert equal area azimuthal' cartographic projection.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Orthographic_projection">Orthographic projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:152px;"><img alt="" src="150px-Ben_Orthographic.jpg" width="150" height="150" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Ben_Orthographic.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Ben_Orthographic.jpg">[*]</a></div>h180° v180°</div></div></div>
<p>This is the view of a sphere, with a panorama mapped to the outside, seen from a far distance.
<br style="clear:both;" />
</p>
<h1><span class="mw-headline" id="Other_projections">Other projections</span></h1>
<h2><span class="mw-headline" id="Cubic_projection">Cubic projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Big_ben_cubic.jpg" width="200" height="150" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_cubic.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_cubic.jpg">[*]</a></div><a href="Cubic_Projection.html" title="Cubic Projection">Cubic Projection</a> h90° v90° per cubeface</div></div></div>
<p>Technically a sub-case of the <a href="Rectilinear_Projection.html" title="Rectilinear Projection">Rectilinear Projection</a>, the cubic projection is used as the source projection for fully spherical Quicktime<a class="external" href="http://wiki.panotools.org/Quicktime">[*]</a> VR panoramas.  See <a href="Cubic_Projection.html" title="Cubic Projection">Cubic Projection</a> for more.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Sinusoidal_projection">Sinusoidal projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Bin_ben_sinusoidal.jpg" width="200" height="100" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Bin_ben_sinusoidal.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Bin_ben_sinusoidal.jpg">[*]</a></div>Sinusoidal Projection<a class="external" href="http://wiki.panotools.org/index.php?title=Sinusoidal_Projection&amp;action=edit&amp;redlink=1">[*]</a> h360° v180°</div></div></div>
<p>Sinusoidal Projection<a class="external" href="http://wiki.panotools.org/index.php?title=Sinusoidal_Projection&amp;action=edit&amp;redlink=1">[*]</a> is an <i>equal area</i> projection which makes it suitable for transmission of spherical images, as supported by the DevalVR<a class="external" href="http://wiki.panotools.org/DevalVR">[*]</a> viewer.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Transverse_mercator_projection">Transverse mercator projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:102px;"><img alt="" src="100px-Big_ben_transverse_mercator.jpg" width="100" height="200" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_transverse_mercator.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Big_ben_transverse_mercator.jpg">[*]</a></div>Transverse Mercator Projection<a class="external" href="http://wiki.panotools.org/index.php?title=Mercator_Projection&amp;action=edit&amp;redlink=1">[*]</a> h147° v360°</div></div></div>
<p>This is a <a href="Projections.html#Mercator_projection">Mercator projection</a> rotated 90 degrees, suitable for a long vertical image.
</p><p>Transverse mercator is limited to a maximum horizontal angle of 180 degrees, though in practice images over 150 degrees are not very usable.
<br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Pannini_projection">Pannini projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:222px;"><img alt="" src="220px-Ben_Equirectangular_panini.jpg" width="220" height="110" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Ben_Equirectangular_panini.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Ben_Equirectangular_panini.jpg">[*]</a></div>h180° v110°</div></div></div>
<p>The Pannini projection, also known as 'Recti-Perspective', 'Panini' or 'Vedutismo', keeps verticals vertical and radial lines straight.  This can impart a strong sense of correct perspective to wide angle views that have a single central vanishing point.  However this projection renders horizontal straight lines as curves.  So-called "squeezed" variants reduce or eliminate that curvature, at the expense of bending the ends of long radial lines.
</p><p><a href="The_General_Panini_Projection.html" title="The General Panini Projection">The General Panini Projection</a> is an adjustable version that can zoom continuously from rectilinear, through the standard Pannini projection, to the even more compressed orthographic cylindrical projection.  It was introduced in early 2009 in the Panini panorama viewer.  The version implemented in the PanoTools library in early 2010 also offers two generally useful flavors of squeeze.  
</p><p>There were two earlier implementations in the PanoTools library, 'panini', which is actually not the Pannini projection but a very similar compressed cylindrical projection, and 'equirectangular panini', which is the standard Pannini, or stereographic cylindrical, projection. 
</p><p><br style="clear:both;" />
</p>
<h2><span class="mw-headline" id="Architectural_projection">Architectural projection</span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><img alt="" src="200px-Ben_Architectural.jpg" width="200" height="82" class="thumbimage" /><a class="external" href="http://wiki.panotools.org/File:Ben_Architectural.jpg">[*]</a>  <div class="thumbcaption"><div class="magnify"><img src="magnify-clip.png" width="15" height="11" alt="" /><a class="external" href="http://wiki.panotools.org/File:Ben_Architectural.jpg">[*]</a></div>h360° v152°</div></div></div>
<p>This is <a href="Projections.html#Miller_projection">Miller projection</a> above the horizon and <a href="Projections.html#Lambert_cylindrical_equal_area">Lambert Equal Area projection</a> below. Suitable for scenes where the the ground isn't very interesting.
<br style="clear:both;" />
</p>
<h1><span class="mw-headline" id="External_links">External links</span></h1>
<ul>
<li> Description of panoramic image projections - <a rel="nofollow" class="external free" href="http://www.cambridgeincolour.com/tutorials/image-projections.htm">http://www.cambridgeincolour.com/tutorials/image-projections.htm</a>
</li>
<li> Two talks from the 2009 Panotools Meeting<a class="external" href="http://wiki.panotools.org/Panotools_Meeting">[*]</a> by the <i>panotwins</i> with a comparison of projection types:
</li>
</ul>
<dl>
<dd>Introduction <a rel="nofollow" class="external free" href="http://pt2009.panobotics.de/index.php?id=163">http://pt2009.panobotics.de/index.php?id=163</a>
</dd>
<dd>Talk #1 by Markus <a rel="nofollow" class="external free" href="http://pt2009.panobotics.de/index.php?id=164">http://pt2009.panobotics.de/index.php?id=164</a>
</dd>
<dd>Talk #2 by Jürgen <a rel="nofollow" class="external free" href="http://pt2009.panobotics.de/index.php?id=165">http://pt2009.panobotics.de/index.php?id=165</a>
</dd>
</dl>
<ul>
<li> xkcd discusses <i>What your favorite map projection says about you</i> - <a rel="nofollow" class="external free" href="http://xkcd.com/977/">http://xkcd.com/977/</a>
</li>
</ul>




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